I hope that I have picked the right images as you did not provide us with any links. My discussion will be based on the images in the links below.
Typically, if images in primary sources differ, you need to ask what the purpose of each artist was. In this case, we can attribute the differences in part to the different goals that the artists had in mind. De Bry's work was more commercial it was meant simply to be sold to people in Europe. By contrast, Eckhout's work was commissioned by the Dutch governor in Brazil. Eckhout would therefore have had less incentive than De Bry to make his works lurid and savage-looking.
It may also be that the differences reflect the fact that De Bry never actually traveled to America. He based his work on his imagination and on accounts from people who had been in America. By contrast, Eckhout worked from real life. This may account also for the more realistic portrayal in his work.